school of economics and management

Carlos Pestana Barros & Nicolas Peypoch

A Comparative Analysis of Productivity Change in Italian and Portuguese Airports

WP 006/2007/DE _________________________________________________________

Susana Santos

Socio-Economic Studies with Social Accounting and Sociodemographic Matrices. An application to Portugal.

WP 16/2013/DE/UECE

_________________________________________________________

Department of Economics

WORKING PAPERS

ISSN Nº 0874-4548

School of Economics and Management TECHNICAL UNIVERSITY OF LISBON

SOCIO-ECONOMIC STUDIES with SOCIAL ACCOUNTING and SOCIO-

DEMOGRAPHIC MATRICES. An application to Portugal.

BY SUSANA SANTOS1

ISEG (School of Economics and Management) of the Technical University of Lisbon

UECE (Research Unit on Complexity and Economics) and DE (Department of Economics).

Abstract

In looking for empirical evidence about the activity of countries, a proposal is made for studying

(measuring and modelling) the activity of countries through the use of Social Accounting Matrices

(SAMs) and Socio-Demographic Matrices (SDMs).

SAMs and SDMs are presented as tools that have specific features for conducting studies in several

different areas, as well as for supporting policy decision processes.

Based on methodological principles that are derived mainly from the works of Richard Stone, emphasis

is placed on the desirability of working in a matrix format, which includes not only people (SDM), but

also, at the same time, activities, products, factors of production and institutions (SAM). This is considered

to be a way of capturing the relevant network of linkages and the corresponding multiplier effects, which

can be used for the subsequent modelling of the activity of the countries studied.

A method will be proposed for the construction of these matrices. In the case of the SAMs, it is proposed

that their design and construction should adopt, at least as their starting point, the latest version of the

System of National Accounts (2008 SNA) and the corresponding results of its adoption/adaptation by

different countries.

The exposition of this proposal is accompanied by an example applied to Portugal.

Key words: Social Accounting Matrix; National Accounts, Socio-Demographic Matrices.

JEL classification: C82; E16; E61; J11.

(September 2013)

Notes:

- The author gratefully acknowledges the financial support provided by FCT (Fundação para a Ciência e a Tecnologia)

Portugal for the research and writing of this article, which forms part of the Strategic Project for 2011-13 (PEst-

OE/EGE/UI0436/2011).

- Part of the description of the SAM-based approach adopted in this paper can also be found in another article by the

same author, which is published in the International Journal of Humanities and Social Science, 10 (2013), pp. 85-

100.

- An identical version of this paper, but with an (attempted) application to Mozambique, can be found in the MPRA

(Munich Personal RePEc Archive) Paper No. 47999, July 2013.

1 Address for correspondence: ISEG /UTL, Rua Miguel Lupi, 20, 1249-078 Lisboa, Portugal ([email protected]).

SOCIO-ECONOMIC STUDIES with SOCIAL ACCOUNTING and SOCIO-DEMOGRAPHIC

MATRICES. An application to Portugal. SSantos

CONTENTS

1. Introduction ............................................................................................................................. 1

2. Looking for empirical evidence about the activity of countries .............................................. 2

3. Approaches based on Social Accounting Matrices (SAMs) and Socio-Demographic

Matrices (SDMs) ...................................................................................................................... 3

4. Constructing SAMs from the SNA .......................................................................................... 6

4.1. The SAM’s basic structure ................................................................................................. 7

4.2. Disaggregations and extensions ...................................................................................... 13

4.3. Aggregates, indicators and balancing items ..................................................................... 20

5. Constructing SDMs .. ............................................................................................................ 22

6. Summary and Concluding remarks ........................................................................................ 27

References ................................................................................................................................... 30

Appendixes .................................................................................................................................. 33



- 1 -

1. Introduction

The Social Accounting Matrix (SAM) and the Socio-Demographic Matrix (SDM) are tools that have

specific features intended for studying the activity of countries. Both matrices cover movements in

time and space, which are expressed by the former matrix in units of currency and by the latter matrix

in terms of human beings.

Such features allow for the reading and interpretation of the reality under study, leading to the

production of an empirical work that is not only capable of highlighting specific aspects of that

activity, but also offer the chance to experiment with different interventions in regard to its

functioning.

A proposal will be made for the development both of a basic SAM and of a standard SDM. Together

with an explanation of possible alternative taxonomies, this presentation will show how those

matrices can be used as an alternative support for studies being undertaken in several areas, as well

as for the work of those taking part in the policy decision process. Underlying the application that

will be made in order to illustrate this presentation is a reality whose interpretation will not extend

beyond a number of examples explaining how those matrices can be used in those cases.

By stating that our knowledge of the activity of countries involves the use of national and

demographic accounts, Section 2 justifies the decision to use the national and the demographic

accounts, as well as the matrix form for studying the empirical evidence of that same activity.

Section 3 adopts a methodological framework that is based on Richard Stone’s works outlining the

main features of the SAM and SDM-based approaches. According to this methodological framework,

SAMs and SDMs can describe the activity of countries either empirically or theoretically, depending

on whether they are presented in a numerical or an algebraic version, respectively.

Adopting the above-mentioned methodological framework, and based on the latest version of the

System of National Accounts (2008 SNA), Section 4 presents a proposal for a SAM structure,

beginning with a basic structure and then showing its potentialities for further development. Firstly,

Section 4.1 presents a basic structure and emphasises the need to ensure its consistency with the whole

system. Such emphasis is then reinforced through the analysis of possible disaggregations and

extensions to that basic structure (Section 4.2). Section 4.3 discusses the different forms of analysis

made possible by the use of aggregates, indicators and balancing items that can be calculated from

such a version and which lie outside the matrix format. In order to test the feasibility of adopting this

proposal for different countries, an application is made of the construction of a numerical SAM to

Portugal.



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In turn, following the methodological framework introduced by Section 3, Section 5 presents a SDM

structure, beginning with a standard structure (as proposed by Richard Stone), and then showing

possibilities for further developments. In keeping with what was done in Section 4, an application is

made of the construction of a numerical SDM for Portugal.

Although both the SAM-based and SDM-based approaches make it possible to work with numerical

versions and algebraic versions (models), greater attention will be paid to the construction of the

numerical versions of both matrices – with the inclusion of more details and applications.

Nonetheless, some works devoted to the modelling of those matrices will also be referred to. On the

other hand, because the SDM is a very recent field of research for the author of this paper, this matrix

is not developed in so much detail as the SAM, despite the many common aspects that are shared

between them both.

Section 6 systematises the main ideas of the other sections and makes some concluding remarks in

an attempt to illustrate to what extent countries can use SAMs and SDMs to study (socio-) economic

systems and support their policy decision processes.

2. Looking for empirical evidence about the activity of countries

Statistics record facts. The activity of a country is a series of facts. Therefore, any attempt to gain

knowledge of those facts calls for the use of statistics. However, the complexity of such activity and

the innumerable facts and statistics that serve to record it frequently make this task rather difficult,

and sometimes render our efforts unfeasible. The challenge lies in defining the best hierarchy of facts,

identifying the correct network of linkages between them, ensuring the availability of statistics and

making use of good working tools. Those working tools should enable us to read the reality under

study and to produce an empirical work that is not only capable of highlighting specific aspects of

that activity, but also offers the chance to simulate different interventions in regard to its functioning.

In his preface to the book “Understanding National Accounts”, Giovannini, E. states: “(…) today’s

national accounts are the core of a modern system of economic statistics, and they provide the

conceptual and actual tool to bring coherence to hundreds of statistical sources available in developed

countries” (Lequiller F., Blades D., 2006: 3). If we accept the truthfulness of this statement, then a

plausible statistical base source of information for studying the part of the activity of a country that

can be expressed in currency units ought to be its national accounts. But such activity also depends

greatly on the population of that country, whose movements are expressed in terms of human beings.

The base source for this latter information will therefore be the demographic accounts, more

commonly known as demographic statistics. This methodology can also be applied to countries that



- 3 -

are not normally considered to be developed, but which nonetheless seek to produce national

accounts. However, although this is not so evident with the demographic accounts, we should bear in

mind that underlying the national accounts is a system that defines which facts should be observed

and how these same facts should be recorded. The existence of such a system will certainly influence

the challenge outlined above. Even so, we will adopt the national accounts as our starting point.

On the other hand, working with the (national and demographic) accounts in a matrix format can be

seen as a convenient way of considering the above-mentioned network of linkages existing between

facts about the activity of countries, which will thus help us to achieve greater analytical content. The

matrix format will also allow for the use of matrix algebra in possible mathematical treatments

associated with the above-mentioned empirical work, enabling us to experiment with different

interventions in regard to the functioning of reality. Some other advantages to be gained from the use

of the matrix format will be identified below.

In looking for empirical evidence about the activity of countries, our proposal for a SAM will

therefore make use of the specific hierarchy of the facts that are supposedly observed through the

system of national accounts. In order to better achieve the same purpose, a SDM that makes use of

the hierarchy of the facts observed through the demographic accounts will also be proposed. This will

make it possible to identify networks of linkages that can be worked upon with different purposes in

mind, always operating within a macro framework. Based upon that work, which exhaustively

explores the features of the national accounts and their underlying system, as well as those of the

demographic accounts, further work can be carried out, discovering alternative hierarchies of facts,

identifying the existence and importance of the non-observed facts, and criticising the way in which

the observed facts are recorded, etc.

As the behaviour of facts is explained by theories, our empirical work will also allow us to either test

or better define these theories.

3. Approaches based on Social Accounting Matrices (SAMs) and Socio-Demographic Matrices

(SDMs)

Richard Stone worked largely with SAMs and SDMs as matrix formats of the national and

demographic accounts. Besides numerical versions, he identified algebraic versions of those same

matrices, which were worked on mainly under the scope of input-output analysis. In keeping with

that work, and due to their similarities, we will call the approach based on SAMs the SAM-based

approach – the term that is normally adopted – and the approach based on SDMs the SDM-based

approach – a term that is not normally adopted, but which will be used here.



- 4 -

Following the work of Richard Stone, Graham Pyatt and Jeffrey Round in particular played a key

role in the study and dissemination of the SAM-based approach.

In the foreword to the book that can now be regarded as a pioneering work in terms of the SAM-

based approach, “Social Accounting for Development Planning with special reference to Sri Lanka”,

Stone stated that the framework of the system of national accounts can be rearranged and “the entries

in a set of accounts can be presented in a matrix in which, by convention (…), incomings are shown

in the rows and outgoings are shown in the columns; and in which, reflecting the fact that accounts

balance, each row sum is equal to the corresponding column sum”. That matrix, with an equal number

of rows and columns, is the SAM, in the construction of which “it may be possible to adopt a

hierarchical approach, first adjusting the entries in a summary set of national accounts and then

adjusting subsets of estimates to these controlling totals”. (Pyatt and Roe, 1977: xix, xxiii).

In turn, in the abstract to his article “A SAM approach to modeling”, Pyatt says: “Given that there is

an accounting system corresponding to every economic model, it is useful to make the accounts

explicit in the form of a SAM. Such a matrix can be used as the framework for a consistent dataset

and for the representation of theory in what is called its transaction form”. In that transaction form

(or TV (transaction value) form), the SAM can be seen “(…) as a framework for theory” and its cells

“(…) can be filled instead with algebraic expressions, which describe in conceptual terms how the

corresponding transaction values might be determined”. Thus, the SAM is used as “the basic

framework for model presentation”. (Pyatt, 1988: 327; 337).

Looking at the question from the perspectives outlined above, it can be said that a SAM can have two

versions: a numerical version, which describes the activity of a country empirically; and an algebraic

version, which describes that same activity theoretically. In the former version, each cell has a specific

numerical value, with the sums of the rows being equal to the sums of the columns. In the latter

version, each cell is filled with algebraic expressions that, together with those of all the other cells,

form a SAM-based model, the calibration of which involves a replication of the numerical version.

In the words of Pyatt, “the essence of (...) the SAM approach to modelling is to use the same SAM

framework for both the empirical and the theoretical description of an economy”. (Pyatt, 1988: 337).

In 1953, with the first and most fundamental contribution written by Stone, the United Nations

recommended the System of National Accounts (SNA), which continued to be published in

successive versions until 2008. Also working on the last two versions of that system, published in

1993 and 2008, were, besides the United Nations, the International Monetary Fund, the World Bank,

the Organisation for Economic Cooperation and Development and the Statistical Office of the

European Communities (Eurostat). Together, they formed the Inter-Secretariat Working Group on

National Accounts (ISWGNA).



- 5 -

This system establishes the rules for measuring the activity of countries or groups of countries, which,

in turn, have been adopted and adapted to specific realities by the corresponding statistical offices.

The construction of algebraic versions (or SAM-based models) can be seen, among others, in Pyatt

(2001; 1988), Pyatt and Roe (1977), Pyatt and Round (1985; 2012) and Santos (2010; 2009).

In their latest article, Pyatt and Round (2012) explore and derive conditions for a phenomenon that

they identify as distributional invariance within a SAM-based model. That phenomenon, which they

also call “the Stone phenomenon”, is associated with the study of a component of the multiplier

effects identified during research into the interrelationship between the structure of production and

the distribution of income in the context of economic development. The implications of those

conditions were identified by the authors in the design of SAMs and in the consequent quality of

results generated via subsequent modelling. Consequently, they conclude by appealing for renewed

efforts to be made in the design and construction of SAMs with a view to obtaining a more realistic

starting point for subsequent modelling.

The SAMs used in the works of reference written about the SAM-based approach were constructed

to deal with specific realities. They were created by teams with access to primary sources of

information, and were designed according to each specific case. However, there are many cases in

which the SAM-based approach is adequate for proceeding with certain studies, even when access to

primary sources of information is not feasible and teams are not available. In view of these

circumstances, special attention has been paid by the author to the construction of numerical versions

of SAMs from the SNA, a subject which will be examined in Section 4.

Despite the potentialities of Stone’s work on SDMs, the SDM-based approach has not been followed

by other authors as much as the SAM-based approach. Thus, the study of the SDM-based approach

will be based only on Stone’s works.

According to this author, the population of a specific country in a specific year “flows in partly along

time from last year, through survival, and partly along space from the outside world, through birth

and immigration; and flows out, through death and emigration, and partly along time into next year,

through survival” (Stone, 1986: 21). With the survivors from the preceding period constituting the

opening stock of the population and the survivors into the succeeding period constituting the closing

stock, the SDM can thus be considered a stock-flow matrix.

By connecting “the opening and closing stocks of year θ with flows during year θ” (Stone, 1982:

292), two types of versions will be identified for the SDM: numerical versions, in which each cell has

a specific numerical value; and algebraic versions, in which each cell is filled with algebraic

expressions that, together with those of all the other cells, form a SDM-based model.



- 6 -

Numerical versions of SDMs can thus be constructed from demographic statistics or they can be

replicated by the running of SDM-based models. The former versions measure the reality under study

and will be examined in Section 5. The latter versions allow for the construction of scenarios resulting

from experiments performed with those models, and can be seen in: Stone, 1966, 1971, 1973, 1975,

1981, 1982, 1985, 1986a.

SDM-based models and the combination of SAM and SDM-based approaches will be part of this

author’s future research work.

4. Constructing SAMs from the SNA.

The latest versions of the SNA have devoted a number of paragraphs to discussing the question of

SAMs. The 2008 version mentions SAMs in Section D of its Chapter 28, entitled “Input-output and

other matrix-based analysis” (ISWGNA, 2009: 519-522), in which a matrix representation is

presented of the accounts identified and described in the whole SNA. This representation is not,

however, to be identified with the SAM presented in this paper, although they both cover practically

all the flows recorded by those accounts.

In turn, the European System of National and Regional Accounts in the European Union of 20102

(the adaptation for Europe of the 2008 version of the SNA) makes a reference to the SAM, stating

that, among other features, it can be thought of as an expanded system of labour (satellite) accounts

(Chapter 22).

The SAM that will be presented below results from the work that the author has undertaken within

the methodological framework presented in Section 3, based especially on the works of Graham Pyatt

and his associates (Pyatt, 1988 and 1991; Pyatt and Roe, 1977; Pyatt and Round, 1985 and 2012), as

well as from the efforts made to reconcile that framework with what has been defined by (the

successive versions of) the SNA (Pyatt, 1985 and 1991a; Round, 2003; Santos, 2009). Thus, the

author will propose a version of the SAM that seeks to be as exhaustive as possible regarding the

flows observed by the SNA. Pyatt (1999) and Round (2003) also approach this same issue with the

use of their own versions.

The following proposal will be accompanied by the applications made of the SAM to Portugal in

2009. In that year, the Portuguese national accounts adopted the European System of National and

Regional Accounts in the European Community of 1995 – the adaptation for Europe of the 1993

version of the SNA. Because the general differences between the accounts identified in those

2 EU Regulation No. 549/2013 of the European Parliament and of the European Council of 21 May 2013, on the European

system of national and regional accounts in the European Union – Official Journal of the European Union, L174, Volume

56, 26 June 2013.



- 7 -

applications and described in the 1993 and 2008 versions of the SNA are not significant, they will be

used to illustrate the following exposition.

Thus, returning to the description provided in Section 3, a square matrix will be worked upon, in

which the sum of the rows is equal to the corresponding sum of the columns. In keeping with what is

conventionally accepted, and after some adjustments have been made to adapt this to the SNA,

resources, incomes, receipts or changes in liabilities and net worth will be represented in the entries

made in the rows, while uses, outlays, expenditures or changes in assets will be represented in the

entries made in the columns. Each flow will therefore be recorded only once, in a cell of its own. The

following description will be made in accordance with the 2008 SNA.

The starting point for the construction of a numerical SAM should be its design, i.e. the classification

or taxonomy of its accounts. That taxonomy and the levels of disaggregation adopted will depend on

the purposes for which the SAM is to be used, as well as on the way that the available information is

organised. Adopting the national accounts as the base source of information, a basic structure is

proposed below, which takes into account the underlying SNA and highlights the consistency of the

whole system. The flexibility of that basic structure will be shown, together with the possibilities that

it presents for characterising problems and for achieving specific purposes. These will also be seen

as possibilities for going beyond the SNA, which is considered as a starting point, as mentioned in

Section 2.

In this respect, we are aware of the dangers associated with the adoption of international standards

and systems of classification and their failure to recognise important issues and realities. This problem

is also mentioned by Pyatt and Round when they consider the choice of taxonomies within a SAM

framework and the strategic influence that these can have on the potential usefulness of subsequent

applications. According to those authors: “the taxonomies that are embedded within [the SAM

framework] predetermine what any subsequent modelling exercise might have to say in response to

specific distributional questions” (Pyatt and Round, 2012: 270).

4.1. The SAM’s basic structure

Adopting the working method recommended by Stone in the second paragraph of Section 3 of this

paper, the basic structure for the SAM presented here will be a summary set of the national accounts

and the controlling totals for the other levels of disaggregation, which will later be analysed in Section

4.2. Thus, in keeping with the conventions and nomenclatures defined by the SNA, besides a rest of

the world account, the proposed SAM will also include both production and institutional accounts.

Table 1 shows the above-mentioned basic structure, representing the nominal transactions (“t”) with

which two indexes are associated. The location of these transactions within the matrix framework is



- 8 -

described by those indexes, the first of which represents the row account while the second represents

the column account. Each cell of this matrix will be converted into a submatrix, with the number of

rows and columns corresponding to the level of disaggregation of the row and column accounts. This

same table also identifies blocks, which are submatrices or sets of submatrices with common

characteristics. The specification of these blocks will be made below and involves an identification

of the flows of the National Accounts, which will continue to be the same even if some disaggregation

is performed – thereby preserving the consistency of the whole system.

Table 1. The Basic SAM by blocks

p a f dic dik dif rw total

p – products TTM

(tp,p) IC

(tp,a) 0

FC

(tp,dic) GCF

(tp,dik) 0

EX

(tp,rw) AD

(tp.. )

a – activities P

(ta,p) 0 0 0 0 0 0

VPT

(ta . )

f – factors 0 CFP_GAV

(tf,a) 0 0 0 0

CFP (tf,rw)

AFIR

(tf . )

dic – (domestic) institutions’

current account

NTP

(tdic,p) NTA

(tdic,a) CFP_GNI

(tdic,f) CT

(tdic,dic) 0 0

CT

(tdic,rw) AI

(tdic. )

dik – (domestic) institutions’

capital account 0 0 0

S

(tdik,dic) KT

(tdik,dik) NLB

(tdik,dif)

KT

(tdik,rw) INVF

(tdik. )

dif – (domestic) institutions’

financial account 0 0 0 0 0

FT

(tdif,dif) FT

(tdif,rw) TFTR

(tdif.)

rw – rest of the world IM&NTP

(trw,p) NTA (trw,a)

CFP (trw,f)

CT

(trw,dic) KT

(trw,dik) FT

(trw,dif) 0

TVRWP

(trw.)

total AS

(t.p)

VCT

(t.a )

AFIP

(t.f )

AIP

(t.dic)

AINV

(t.dik )

TFTP

(t.dif)

TVRWR

(t..rw )

Source: Santos (2009; 2010)

Note: The first three accounts (p = products (or goods and services), a = activities (or industries) and

f = factors (of production)) are the production accounts of the economy and the next three

accounts (dic = current; dik = capital; dif = financial) are the accounts of the (domestic)

institutions. The last account (rw = rest of the world) represents the “outside” part of the

(domestic) economy.

Description of the blocks (included in the texts are letters followed by numbers between brackets,

which are the flow codes of the National Accounts, in accordance with the 2008 SNA):

a) Production – P (cell: ta,p; basic prices) – represents the output of goods and services (P1).

b) Domestic Trade is represented by the value of domestically transacted products, which can be

either domestically produced or imported.



- 9 -

b.1) Intermediate Consumption – IC (cell: tp,a; purchasers’ prices) – consists of the value of the

goods and services consumed as inputs by a process of production, excluding those fixed

assets whose consumption is recorded as consumption of fixed capital (P2).

b.2) Final Consumption – FC (cell: tp,dic; purchasers’ prices) – consists of the expenditure incurred

by resident institutional units on goods or services that are used for the direct satisfaction of

individual needs or wants, or the collective needs of members of the community (P3).

b.3) Gross Capital Formation – GCF (cell: tp,dik; purchasers’ prices) – includes gross fixed capital

formation, changes in inventories, and acquisitions less disposals of valuables (P5).

c) External Trade includes the transactions in goods and services from non-residents to residents,

also known as imports (P7), or IM (cell: trw,p; purchasers’ prices), and the transactions in goods

and services from residents to non-residents, also known as exports (P6), or EX (cell: tp,rw;

purchasers’ prices).

d) Trade and Transport Margins – TTM (cell: tp,p) – amounts to zero and, when it is disaggregated

and takes the form of a submatrix, it allocates the output of the trade and transport services used

in the domestic trade to the supplied products.

e) Net taxes on production and imports

e.1) Net Taxes on Production – NTA (cells: tdic,a; trw,a) – represents the (other) taxes on production

(D29) minus the (other) subsidies to production (D39).

e.2) Net Taxes on Products – NTP (cells: tdic,p; trw,p) – represents the taxes on products (D21)

minus the subsidies on products (D31).

f) Compensation of Factors of Production – CFP (cells: tf,a; tdic,f; tf,rw; trw,f) – consists of the income

of the institutional sectors originating from the compensation of employees (D1) and the

compensation of employers and own-account (or self-employed) workers, and the compensation

of capital, including property income (D4; B2g-B3g). The functional distribution is represented

by the Gross Added Value – GAV (cell: tf,a), whereas the institutional distribution is represented

by the Gross National Income – GNI (cell: tdic,f).

g) Current Transactions – CT (cells: tdic,dic; tdic,rw; trw,dic) – includes: current taxes on income, wealth,

etc. (D5); net social contributions (D61); social benefits other than social transfers in kind (D62);

other current transfers (D7); and the adjustment made for the change in pension entitlements (D8).



- 10 -

h) Capital Transactions – KT (cells: tdik,dik; tdik,rw; trw,dik) – includes: capital taxes (D91); investment

grants (D92); other capital transfers (D99); and acquisitions less disposals of non-financial non-

produced assets (NP1-3).

i) Financial Transactions – FT (cells: tdif,dif; tdif,rw; trw,dif) – includes: monetary gold and special

drawing rights (F1); currency and deposits (F2); debt securities (F3); loans (F4); equity and

investment fund shares (F5); insurance, pension and standardised guarantee schemes (F6);

financial derivatives and employee stock options (F7); and other accounts receivable/payable

(F8).

j) Gross Saving – S (cell: tdik,dic) – measures the portion of aggregate income that is not used for

final consumption expenditure and current transfers to domestic institutions or to the rest of the

world (B9g).

k) Net Borrowing/Lending – NLB (cell: tdik,dif)

The net lending or borrowing of the total economy is the sum of the net lending or borrowing of

the institutional sectors. It represents, respectively, the net resources that the total economy makes

available to the rest of the world or the net resources that it receives from the rest of the world to

finance the corresponding needs of investment funds (B9).

Here, those amounts are recorded in the row(s) of the capital account, i.e. as changes in liabilities

and net worth, and in the column(s) of the financial account, i.e. as changes in assets. This is why

the mathematical signs of this item have been changed in relation to the SNA.

The construction of a SAM is easier when it is performed by blocks.

The totals of each account represent the corresponding sums of the cells in rows and in columns, with

the following description:

I. Products account (p): Aggregate Demand – AD, the row sum (cell: tp.); Aggregate Supply – AS,

the column sum (cell: t.p).

II. Activities account (a): Production Value – VPT, the row sum (cell: ta.); Total Costs – VCT, the

column sum (cell: t.a).

III. Factors of Production (f): Aggregate Factors Income (Received) – AFIR, the row sum (cell: tf.);

Aggregate Factors Income (Paid) – AFIP, the column sum (cell: t.f).

IV. Current account of (domestic) institutions (dic): Aggregate Income (received) – AI, the row sum

(cell: tdic.); Aggregate Income (Paid) – AIP, the column sum (cell: t.dic).



- 11 -

V. Capital account of (domestic) institutions (dik): Investment Funds – INVF, the row sum (cell:

tdik.); Aggregate Investment – AINV, the column sum (cell: t.dik).

VI. Financial account of (domestic) institutions (dif): Total Financial Transactions (Received) –

TFTR, the row sum (cell: tdif.); Total Financial Transactions (Paid) – TFTP, the column sum (cell:

t.dif).

VII. Rest of the world account (rw): Value of Transactions to the Rest of the World (Paid) – TVRWP,

the row sum (cell: trw.); Value of Transactions from the Rest of the World (Received) – TVRWR,

the column sum (cell: t.rw).

From the above description, two further advantages of the matrix presentation of the national accounts

can be highlighted: each transaction represents a single entry and can be characterised by its position;

each account is represented by a row and a column, whose balance is ensured by the equality of their

sums.

The Integrated Economic Accounts Table is equivalent to a summary of what is observed by the SNA.

According to the 2008 SNA: “The integrated economic accounts use (…) three of the conceptual

elements of the SNA (...) [institutional units and sectors, transactions, and assets and liabilities]

together with the concept of the rest of the world to form a wide range of accounts. These include the

full sequence of accounts for institutional sectors, separately or collectively, the rest of the world and

the total economy…. This table shows, simultaneously, the general accounting structure of the SNA

and presents a set of data for the institutional sectors, the economy as a whole and the rest of the

world” (ISWGNA, 2009: 23; 29). Based on this table and the previous description (adapted to the

previous version of the SNA), it was possible to construct the basic SAM presented in Table 2,

representing the highest possible level of aggregation of the activity of Portugal observed by the

national accounts in 2009.



- 12 -

Table 2. Basic SAM of Portugal in 2009

(Unit: 106 euros)

p a f dic dik dif rw total

p – products 0 162 661 146 934 34 051 47 236 390 882

a – activities 311 365 311 365

f – factors 149 403 9 039 158 443

dic – (domestic) institu-

tions’ current account 19 694 522 141 423 85 711 4 581 251 931

dik – (domestic) institu-

tions’ capital account 15 865 1 536 16 222 2 232 35 856

dif – (domestic) institu-

tions’ financial account 36 659 37 209 73 868

rw – rest of the world 59 823(a) - 1 222 17 019 3 421 268 20 987 100 297

total 390 882 311 365 158 443 251 931 35 856 73 868 100 297

Sources: Statistics Portugal (INE); Portuguese Central Bank (Banco de Portugal).

(a) 59 717 (imports) + 106 (net taxes on products sent to the institutions of the European Union)

Considering the description given about Table 1, and based on the reading of the products account in

Portugal in 2009, represented in Table 2 – row and column p, the main components of the aggregate

demand and supply of the goods and services transacted in the market and captured by the Portuguese

National Accounts, can be identified in millions of euros. Thus, reading in rows, the total aggregate

demand of 390,882 million euros was composed of 162,661million euros of intermediate

consumption, 146,934 million euros of final consumption, and 34,051 million euros of gross capital

formation and 47,236 million euros of exports. Reading in columns, the total aggregate supply of

390,882 million euros (equal to the total aggregate demand) was composed of 311,365 million euros

from the output of goods and services, 19 694 million euros of net taxes on products received by the

Portuguese Government and 59,717 million euros of imports and 106 million euros of net taxes on

products sent to the institutions of the European Union. A similar reading can be made for each of

the other columns and rows of Table 2 for Portugal.

Therefore, as mentioned above, and again using the words of Stone, the basic SAM that has just been

described can be considered as the most aggregate “summary set of national accounts”, representing

a first level of the intended hierarchical method, with all the controlling totals for the next level of

that hierarchy. From here the consistency of the whole (supposedly) observed system can be ensured.



- 13 -

From the above description, two further advantages of the matrix presentation of the national accounts

can be highlighted: each transaction represents a single entry and can be characterised by its position;

each account is represented by a row and a column, whose balance is ensured by the equality of their

sums.

4.2. Disaggregations and extensions

Since the national accounts cover all the details covered by the basic structure presented above, some

other levels of the above mentioned-hierarchical method can be identified within the national

accounts, providing other controlling totals for greater levels of disaggregation. As will be seen

below, this disaggregation can be made at the levels of the production, institutional and rest of the

world accounts, either within the scope of the SNA conventions or not. Reverse reasoning can be

applied to the case of aggregation. Therefore, in addition to the already-mentioned advantages of

presenting the national accounts in the form of a matrix, it is also possible to make an easier

aggregation and disaggregation of the accounts, in accordance with the specific requirements of the

exercise and the available information, without losing the consistency of the system.

In the words of Round, in his Foreword to Santos (2009): “The key to constructing a useful SAM and

developing an effective SAM-based model is the SAM design. A SAM need not be dimensionally

large as long as it represents the most significant features of economy-wide interdependence. More

precisely, this means designing the SAM so that the key sectors, markets and institutions are as fully

represented as is practicable. Estimation of the transactions between accounts is obviously also

important but this needs to go in tandem with the SAM design” (Santos, 2009: xiv).

It is also worth mentioning that, although the quarterly national accounts are not as complete as the

annual ones, it will nonetheless be possible to make some further disaggregations from these accounts

in terms of time.

Furthermore, disaggregations can be made in terms of space, since regional accounts are also

considered. In that case, it is possible to work with regions and countries, either individually or as a

group. Round (1991; 1994), for example, experimented with the case of Europe. It would even be

possible to think in world terms, if the SNA could be adopted worldwide.

Extensions are also possible, either from the national accounts or from other sources of information,

with the convenient adjustment to, or connection with, the whole system in order to maintain its

consistency.

The 2008 SNA dedicates its Chapter 29 to “Satellite accounts and other extensions” (ISWGNA, 2009:

523-544)3, where the main idea is to serve specific analytical purposes, in a way that is consistent

3 The 2010 ESA dedicates its Chapter 22 to that same subject (see footnote 1).



- 14 -

with the central framework, although not fully integrated into it (ISWGNA, 2009: 37-38). In this

respect, the author would like to support Steven Keuning and Willem Ruijter’s idea of a “complete

data set” which “could be tentatively labelled: a System of Socio-economic Accounts” (Keuning and

Ruijter, 1988: 73).

4.2.1. Production accounts

In the basic structure proposed in Section 4.1, the production accounts are the accounts of products,

activities and factors of production. These accounts correspond respectively to the SNA accounts of

goods and services, production and the primary distribution of income. Thus, within these accounts

and depending on the available level of disaggregation, it can be seen how the available products are

used, with some details being provided about the process of production and about the way in which

the incomes resulting from that process and the ownership of assets are distributed among institutions

and activities.

The SNA uses the Central Product Classification (CPC) Version 2 (completed in December 2008) to

classify products (ISWGNA, 2009: 19), which are organised into 10 sections, with it being possible

to go as far as the fifth level of disaggregation within each of these.

In turn, the International Standard Industrial Classification of All Economic Activities (ISIC)

Revision 4 (officially released in August 2008) is used to classify activities (ISWGNA, 2009: 20),

organised into 23 sections, the disaggregation of which is perfectly consonant with that of the product

classification. The Supply and Use Table provides this information, usually at an intermediate level

of disaggregation.

As described above, in the characterisation of the block representing the compensation of the factors

of production, the disaggregation that can be made from the already mentioned tables of the national

accounts is between labour (or the compensation of employees) and what has been referred to as the

compensation of other factors, which includes the compensation of employers and own-account (or

self-employed) workers, and the compensation of capital, namely property income. Such information

can only be derived from the Integrated Economic Accounts Table if the products and activities

accounts are not disaggregated, or from the Supply and Use Table if those same accounts are

disaggregated. Table 3, which contains the above-mentioned application to Portugal, in which the

products and activities accounts are not disaggregated, presents the possible disaggregation of the

factors of production accounts based on the Integrated Economic Accounts Table.

Regarding the design of SAMs and in order to establish a connection between the taxonomies dealt

with in this section and in the next, it should be mentioned that in their latest work, besides a rest of

the world account, Pyatt and Round identify accounts for goods and non-factor services and factor



- 15 -

services, as well as, accounts for institutions. In the latter, they identify private and public sector

current accounts and combined capital accounts. About this classification, they say the following:

“taxonomies for goods and services serve to distinguish different markets and should therefore be

constructed in ways that recognise significant market failures and segmentation. In contrast, the

institutions within the private sector are differentiated by the assets they own (or do not own…) and

the productive activities they are responsible for…. Factors of production and the assets that provide

them are therefore the defining feature of institutions.” (Pyatt and Round, 2012: 268).

4.2.2. Institutions and Rest of the World accounts

In the basic structure proposed in Section 4.1, the domestic institutions are divided into current,

capital and financial accounts. These accounts correspond, respectively, to the following SNA

accounts: secondary distribution of income, redistribution of income in kind and use of income;

capital; and financial accounts. Within these accounts, depending on the level of disaggregation

available, the current accounts show how the national income is transformed into disposable income

through the receipt and payment of current transfers, and how the latter is distributed between final

consumption and saving. In turn, the capital account records the transactions linked to acquisitions of

non-financial assets and capital transfers involving the redistribution of wealth, whereas the financial

account records the transactions in financial assets and liabilities between institutional units, and

between these and the rest of the world.

All the linkages between the domestic economy and the rest of the world, i.e. all the transactions

between resident and non-resident units, are recorded both in the SAM and in the SNA through the

rest of the world account.

Chapter 4 of the 2008 SNA specifies the institutional sectors, including the rest of the world, and their

possible disaggregation, which in some cases can be taken as far as the third level (ISWGNA, 2009:

61-85), although normally it cannot be taken beyond the first level. In the case of the rest of the world,

such disaggregation will certainly depend on the country, or group of countries, that adopt and adapt

this system4.

At the first level of disaggregation, the accounts of the institutions, as well as the rest of the world

account, are part of the Integrated Economic Accounts Table. Higher levels of disaggregation,

whenever these are possible, are usually published in the separate accounts of institutions. Even at

the first level of disaggregation, any work conducted with the institutional sectors when there are

4 In the case of the 2010 ESA (Chapter 23), a second level of disaggregation is made, with a distinction being drawn

between Member States and institutions and bodies of the European Union and non-member countries and international

organisations that are not resident in the European Union. For the former, the disaggregation can be made as far as the

fourth level (see footnote 1).



- 16 -

transactions involving more than one row or column of the SAM also requires the so-called “from

whom to whom matrices”. These matrices make it possible to fill in the cells of the submatrices of

transactions taking place within domestic institutions and between institutions and the rest of the

world, recorded in the above-described blocks of current, capital, and financial transactions (Section

4.1 g-i). For the application to Portugal, the connection between the totals of the current transactions

block of the SAM (Table 3) and the Integrated Economic Accounts Table (Appendix A) can be

identified in Appendix B, with all its cells being filled in from the “from whom to whom matrices”

of the transactions included in the block (current taxes on income, wealth, etc.; social contributions,

etc.).

The disaggregation of specific institutional sectors makes it possible to analyse the most diverse

aspects of the corresponding roles in the activity of countries (Santos (2004) and (2007) are examples

of studies on the role of the general government and its subsectors – central government, local

government and social security funds).

The detailed study of the specific accounts of domestic institutions and their corresponding

transactions also makes it possible to analyse specific aspects of that same activity: the distribution

and redistribution of income, using the current account; the redistribution of wealth, using the capital

account; investment, its financing, and the implicit levels of the financing requirements and

availability of the institutional sectors and the whole economy, using the capital and financial

accounts.

In turn, the rest of the world account can provide many possibilities for studying the international

economic relations of the domestic economy.

Table 3 presents the possible disaggregation of the institutions’ current and capital accounts, made

from the Integrated Economic Accounts Table and the “from whom to whom matrices”, for the

above-mentioned application. From that table, we can discover a little more about the reality under

study – Portugal in 2009. This is the case with the aggregate factors income – the so-called primary

distribution of income, to the amount of 158,443 million euros, in which it can now be seen that

86,127 million euros account for the compensation of employees – row and column 3, and 72,315

million euros account for the compensation of other factors of production, namely employers and

own-account workers, land and capital (including property income) – row and column 4.

Through row 3 we can see that 85,888 million euros represent the part of the gross added value,

generated in the domestic economy by residents and non-residents that is attributed to the

compensation of employees, to which are added 239 million euros generated abroad by residents. In

turn, row 4 shows that 63,515 million euros represent the part of the gross added value, generated in

the domestic economy by residents and non-residents, that is attributed to the above-mentioned other



- 17 -

factors of production, to which are added 8,800 million euros generated abroad by residents. Rows 3

and 4 allow for the study of aspects related with the functional distribution of income.

Through column 3, we can see that 85,757 million euros represent the part of the gross national

income, generated in the domestic economy and abroad by residents, that is attributed to the

compensation of employees, to which are added 370 million euros generated in the domestic economy

by non-residents and sent abroad. In column 4, we can see that 55,666 million euros is the part of the

gross national income, generated in the domestic economy and abroad by residents, that is attributed

to the compensation of other factors, to which are added 16,649 million euros generated in the

domestic economy by non-residents and sent abroad. From the cells of columns 3 and 4, it is possible

to study aspects related to the institutional distribution of income.

Just as the matrix form of the production accounts may be easily worked on from the supply and use

tables, it would also be possible to work on the matrix form of the institutional accounts if some kind

of “from whom to whom tables” were made official. This would be a crucial factor for implementing

the SAM-based approach, in which SAMs with production and institutional accounts, conveniently

capturing the circular flow of income and the underlying network of linkages, would form the basis

for macroeconomic models capable of reproducing the multiplier processes implicit in the activity of

countries.

SOCIO-ECONOMIC STUDIES with SOCIAL ACCOUNTING and SOCIO-DEMOGRAPHIC MATRICES. An application to Portugal. SSantos

- 18 -

Table 3. SAM of Portugal in 2009, with disaggregated factors of production and the (domestic) institutions’ current and capital accounts

(Unit: 106 euros) Outlays (expenditures)

Incomes (receipts)

PRODUCTION INSTITUTIONS

PRODUCTS ACTIVITIES

FACTORS CURRENT ACCOUNT

Labour

(employees) Other

Total Households

Nonfinancial

corporations

Financial

corporations Government NPISH

Total

1 2 3 4 5 6 7 8 9

PR

OD

UC

TIO

N

PRODUCTS 1 0 162 661 0 0 0 106 206 0 0 37 160 3 568 146 934

ACTIVITIES 2 311 365 0 0 0 0 0 0 0 0 0 0

FA

CT

OR

S Labour (employees) 3 0 85 888 0 0 0 0 0 0 0 0 0

Other 4 0 63 515 0 0 0 0 0 0 0 0 0

Total 0 149 403 0 0 0 0 0 0 0 0 0

INS

TIT

UT

ION

S

CU

RR

EN

T A

CC

OU

NT

Households 5 0 0 85 757 34 258 120 015 801 1 830 5 226 28 998 95 36 949

Nonfinancial corporations 6 0 0 0 14 615 14 615 1 830 0 613 171 0 2 613

Financial corporations 7 0 0 0 5 990 5 990 5 289 519 131 42 32 6 013

Government 8 19 694 522 0 - 34 - 34 31 224 5 684 671 8 22 37 610

NonProfitInstitutionsServing

Households(NPISH) 9 0 0 0 837 837 324 154 50 1 997 0 2 525

Total 19 694 522 85 757 55 666 141 423 39 468 8 187 6 690 31 215 150 85 711

CA

PIT

AL

AC

CO

UN

T Households 10 0 0 0 0 0 13 728 0 0 0 0 13 728

Nonfinancial corporations 11 0 0 0 0 0 0 8 903 0 0 0 8 903

Financial corporations 12 0 0 0 0 0 0 0 5 283 0 0 5 283

Government 13 0 0 0 0 0 0 0 0 - 11 695 0 - 11 695


Households(NPISH) 14 0 0 0 0 0 0 0 0 0 - 354 - 354

Total 0 0 0 0 0 13 728 8 903 5 283 - 11 695 - 354 15 865

FINANCIAL ACCOUNT 15 0 0 0 0 0 0 0 0 0 0 0

REST OF THE WORLD 16 59 823 - 1 222 370 16 649 17 019 1 345 240 110 1 726 0 3 421

TOTAL 390 882 311 365 86 127 72 315 158 443 160 747 17 331 12 082 58 407 3 363 251 931



- 19 -

Table 3 (continued). SAM of Portugal in 2009, with disaggregated factors of production and the (domestic) institutions’ current and capital accounts

(Unit: 106 euros) Outlays (expenditures)

Incomes (receipts)

INSTITUTIONS

REST OF THE

WORLD TOTAL

CAPITAL ACCOUNT

FINANCIAL

ACCOUNT

Households Nonfinancial

corporations Financial

corporations Government NPISH Total

10 11 12 13 14 15 16

PR

OD

UC

TIO

N PRODUCTS 1 7 269 19 812 1 064 5 071 834 34 051 0 47 236 390 882

ACTIVITIES 2 0 0 0 0 0 0 0 0 311 365

FA

CT

OR

S

Labour (employees) 3 0 0 0 0 0 0 0 239 86 127

Other 4 0 0 0 0 0 0 0 8 800 72 315

Total 0 0 0 0 0 0 0 9 039 158 443

INS

TIT

UT

ION

S

CU

RR

EN

T A

CC

OU

NT

Households 5 0 0 0 0 0 0 0 3 783 160 747

Nonfinancial corporations 6 0 0 0 0 0 0 0 103 17 331

Financial corporations 7 0 0 0 0 0 0 0 79 12 082

Government 8 0 0 0 0 0 0 0 615 58 407


Households(NPISH) 9 0 0 0 0 0 0 0 1 3 363

Total 0 0 0 0 0 0 0 4 581 251 931

CA

PIT

AL

AC

CO

UN

T Households 10 0 0 53 139 0 192 - 9 004 177 5 093

Nonfinancial corporations 11 0 0 0 795 0 795 11 407 924 22 029

Financial corporations 12 0 0 53 24 0 77 - 4 157 0 1 202

Government 13 3 95 28 0 2 129 17 135 1 118 6 687


Households(NPISH) 14 0 0 0 344 0 344 840 14 844

Total 3 95 135 1 301 2 1 536 16 222 2 232 35 856

FINANCIAL ACCOUNT 15 0 0 0 0 0 0 36 659 37 209 73 868

REST OF THE WORLD 16 - 2 179 2 122 3 315 8 268 20 987 100 297

TOTAL 5 093 22 029 1 202 6 687 844 35 856 73 868 100 297




- 20 -

4.3. Aggregates, indicators and balancing items

As was seen above, practically all the transactions of the national accounts are covered by the SAM,

so that macroeconomic aggregates, indicators and balancing items can be identified from it (see the

description of the cells or blocks in Table 1, as well as Tables 2 and 3 for the application to Portugal).

Gross Domestic Product at market prices (GDPpm), which is usually considered the main

macroeconomic aggregate, can be calculated in the three known approaches:

Gross Domestic Product at market prices (GDPpm), which is usually considered the main

macroeconomic aggregate, can be calculated in the three known approaches:

- Production approach: GDPpm = P – IC + NTP = ta,p – tp,a + (tdic,p+ (part of) trw,p);

- Expenditure approach: GDPpm = FC + GCF + Ex – IM = tp,dic + tp,dik + tp,rw – (part of) trw,p;

- Income approach: GDPpm = GAV + NTP + NTA = tf,a + (tdic,p+ (part of) trw,p) + (tdic,a + trw,a).

The Portuguese GDPpm in 2009 was 168 504 * 106 euros, which can be calculated from these three

approaches as follows:

- Production approach: GDPpm = 311 365 – 162 661 + (19 694 + 106);

- Expenditure approach: GDPpm = 146 934 + 34 051 + 47 236 – 59 717;

- Income approach: GDPpm = 149 403 + (19 694 + 106) + (522 – 1 222).

Domestic Product can be converted into National Product by adding the compensation of factors

received from the rest of the world and deducting the compensation of factors and the net indirect

taxes (on both products and production) sent to the rest of the world, when these exist. Thus, from

the described cells of the basic SAM, GDPpm can be converted into Gross National Product at market

prices (GNPpm) or Gross National Income (GNIpm), as follows: GDPpm + tf,rw – trw,f – trw,a– (part of)

trw,p. On the other hand, as the SAM directly provides Gross National Income, this can also be

calculated just by adding the net indirect taxes (on both products and production) received by

domestic institutions: tdic,f + tdic,p + tdic,a. The corresponding amount for Portugal in 2009 is 161 639 *

106 euros, for which the underlying calculations are as follows: GNPpm= 168 504 + 9 039 – 17 019 –

(–1 222) – 106; GNIpm= 141 423 + 19 694 + 522.

Disposable Income (Domestic or National) is also very important and can be calculated by adding to

GNIpm the net current transactions received by domestic institutions: GNIpm + ((received)tdic,dic+

tdic,rw) – ((paid) tdic,dic+ trw,dic). In our application to Portugal: 161 639 + (85 711 + 4 581) – (85 711 +

3 421) = 162 800 * 106 euros.

In turn, gross aggregates can be converted into net aggregates (and balancing items) by deducting the

consumption of fixed capital, which lies outside the basic SAM but is part of the integrated economic

accounts.



- 21 -

Gross Saving (S) and Net Lending or Borrowing (NLB) are given directly by the SAM, through tdik,dic

and tdik,dif, respectively, which in the case of Portugal in 2009 are: 15 865 and 16 222 * 106 euros. As

explained in Subsection 4.1 - k), the latter amount represents Net Borrowing.

It is also possible to calculate structural indicators of the functional and institutional distribution of

generated income, as well as indicators of the use of disposable income.

In the functional distribution of generated income, the distribution of gross added value – GAV –

among the factors of production is given by the structure of the submatrix in cell tf,a of the basic

structure, with its level of detail depending on the disaggregation of the activities (column account)

and of the factors of production (row account). Table 4 shows the results for the applications to

Portugal.

Table 4. Portuguese functional distribution of the income generated in 2009 (in percentage terms)

%

Factors of Production (generated income = gross added value or gross domestic product)

Labour (employees)

57.5

Other (employers and own-account workers; capital)

42.5

Total 100.0

Source: Table 3

In the institutional distribution of generated income, the distribution of gross national income – GNI

– is given by the structure of the submatrix in cell tdic,f of the basic structure. In this case, the level of

detail will depend on the disaggregation of the factors of production (column account) and of the

current account of the domestic institutions (row account). Table 5 shows the results of our

application.

Table 5. Portuguese institutional distribution of the income generated in 2009 (in percentage terms)

Factors of Production

Labour (employees)

Other (employers and own-account

workers; capital)

Total

Institutions (generated income = gross national income)

Households 100.0 61.5 84.9

Non-financial corporations 26.3 10.3

Financial corporations 10.8 4.2

General government - 0.1 0.0

Non-profit institutions serving

households 1.5 0.6

Total 100.0 100.0 100.0

Source: Table 3



- 22 -

As described above for the whole economy, the disposable income of the institutional sectors can be

calculated in the same way, and then its distribution and use can also be studied – see Table 6.

Table 6. Portuguese distribution and use of disposable income among institutions in 2009 (in

percentage terms)

Distribution of

Disposable

Income

Use of Disposable Income

Final Consumption

Expenditure Saving

Households 73.7 88.6 11.4

Non-financial corporations 5.5 --- 100.0

Financial corporations 3.2 --- 100.0

General government 15.6 145.9 - 45.9

Non-profit institutions serving households 2.0 111.0 - 11.0

Total 100.0 90.3 9.7

Source: Table 3

The main items in the revenue and expenditure of the institutional sectors and of the rest of the world

can be calculated from the respective rows and columns of the SAM. In the case of institutional

sectors, the total balancing item is the net lending/borrowing (NLB) of the respective institutional

sector, with an opposite mathematical sign to the one registered in the SAM; the current balancing

item is the respective gross saving (S); and the capital balancing item is the difference between the

first and the second.

5. Constructing SDMs.

From what was stated in Section 3, just as in any SAM, time and space dimensions can also be

identified in any SDM. With an equal number of rows and columns, in each SDM “in any period, the

equality of inflows and outflows implies that the difference between the opening and the closing

stocks is equal to the net inflow from the outside world” (Stone, 1986: 21). Thus, the SDM connects

the opening and the closing stocks of year θ with the flows during the year θ.

In the standard stock-flow SDM, presented in Table 7, the state at New Year θ or θ+1 refers to the

position on the 1st of January each year.



- 23 -

Table 7: The standard SDM

(Unit: number of individuals)

State at New Year θ

State at New Year θ+1 Outside World

Our Country:

Opening States

Closing

Stocks

Outside World α ď

Our Country: Closing States b S Λn

Opening Stocks n’

Source: Stone (1981, 1982, 1986)

Key:

� α (scalar) = individuals who both enter and leave our country during year θ and so are not recorded

in either the opening or the closing stock of that year (babies born in our country during year θ

who die in our country or emigrate before the end of it; immigrants into our country during year θ

who died in our country or emigrate before the end of it).

� ď (row vector) = individuals who leave our country during year θ and so are recorded in the

opening stock but are not included in the closing stock (deaths and emigrants of year θ).

� b (column vector) = individuals who enter our country during year θ and so are recorded in the

closing stock but are not included in the opening stock (births and immigrants of year θ).

� S (square matrix) = individuals who survive in our country through year θ and so are recorded in

both the opening and the closing stocks (classified by their opening states in the columns and by

their closing states in the rows).

� Λn (column vector) = closing stock in each state.

� n’ (row vector) = opening stock in each state.

The taxonomic framework, within which each study is developed, will depend not only on its

purposes, but also on the information available. The whole population must, however, be included.

There is no doubt about the complexity of this work and the difficulty of obtaining credible and

adequate statistical data.

As seen above, besides the opening and closing stocks, the SDM also quantifies (for each year) the

flows of individuals, which are recorded under “our country: (opening or closing) states”, defined in

accordance with the taxonomic framework adopted. As far as those flows are concerned, adopting

the words of Stone, “Each year individuals can enter a state in several ways: by survival in that same

state from last year, by moving into it from a different state in the course of the year, by birth or by

immigration; and they may leave it by survival into the year, by moving into another state during the

year, by emigration or by death” (Stone, 1986: 22).



- 24 -

Active or passive sequences can be adopted within this framework. In the case of active sequences,

different population groups can be identified, including those who are learning – schoolchildren and

students; those who are earning – members of the labour force, who participate in the market; and the

rest – all the educationally and economically inactive (in the sense that they do not participate in the

labour market and do not produce goods and services transacted in the market). Passive sequences

cover socio-economic groups, which may include such considerations as income, social class, family

size, etc.

The identification of different age groups can be regarded as the necessary step to be taken before

working with an active or a passive sequence.

In the following application to Portugal in 2009, in order to better deal with the above-mentioned

complexity and to study the so-called economic activity of the population, two levels of

disaggregation were identified. At the first level of disaggregation, the population was organised by

age groups. At the second level of disaggregation, within each age group, the population was

classified as either active or inactive, in accordance with their economic activity, understood as their

participation both in the labour market and in the supply side of the goods and services market. With

this process of organisation, the difficulty of obtaining data led, in some cases, to the adoption of

estimates and assumptions in order to be able to complete the matrices. The hierarchical method,

adopted in the previous section (for the construction of the SAM), was adopted. According to this

method, each level of disaggregation has all the controlling totals for the next level of that hierarchy.

The specification of the sources and the methodologies adopted in the construction of the following

SDMs are available in the Appendixes C and D.

Table 8: SDM of Portugal in 2009 – first level of disaggregation: by age group.

(Unit: 103 individuals)

State at 31/12/2008

State at 31/12/2009

Outside

World

Population in Portugal by age group Closing

Stock 0-14 15-24 25-64 65 and over

Outside World 5 5 25 81 10 638

Population

in Portugal

by age

group

0-14 105 1 510 1 615

15-24 10 110 1 070 1 190

25-64 16 146 5 790 5 952

65 and over 0 108 1 772 1 881

Opening Stock 10 623 1 625 1 221 5 924 1 853

Source: Table D.



- 25 -

In the first age group of the population in Portugal in 2009, represented in Table 8 – column and row

0-14, we can see the stocks and the flows of children aged 0 to 14, measured in thousands of

individuals. Thus, reading by columns, the opening stock of children was 1,625; of these, 4 died or

emigrated, 1,510 remained in that age group throughout the year and 110 moved to the 15-24 age

group. Reading by rows, the closing stock was 1,615, which is composed of 105 children surviving

births and immigrants and 1,510 children who have not changed state. A similar reading can be made

for each of the other columns and rows.

The next level of disaggregation will look at the economic activity (as described above) of the

population in Portugal in 2009, within each age group and as represented in Table 9. As was seen

above, the economically active population amounts to those people that participate in the labour

market and/or produce goods and services transacted in the market. Reading the column of the active

15-24 age group, we can see that the opening stock of the active population aged 15 to 24, measured

in thousands of individuals, was 508; of these, 5 died or emigrated, 456 remained in the same situation

throughout the year and 47 moved to the active 25-64 age group. Reading the row for the same age

group, the closing stock was 466, which is composed of 10 immigrants, and 456 who have not

changed state. As was stated for the previous level of disaggregation, a similar reading can be made

for each of the other columns and rows.

The above-described work with population movements within a country, during a specific period

captured by a SDM, can complement and improve the information that has been captured by a SAM

regarding the production, consumption and income of the institutional sector of households.


- 26 -

Table 9: SDM of Portugal in 2009 - second level of disaggregation: by age group and economic activity.


Outside

World

Population in Portugal by age group and economic activity Closing

Stock 0-14 15-24 25-64 65 and over

Active Inactive Total Active Inactive Total Active Inactive Total

Outside World 5 5 5 22 3 25 42 39 81 10 638

Popula

tion i

n P

ort

ugal

by a

ge

gro

up a

nd e

conom

ic

acti

vit

y

0-14 105 1 510 1 615

15-2

4

Active 10 456 466

Inactive 110 614 724

Total 10 110 1 070 1 190

25-6

4

Active 16 47 4 734 4 797

Inactive 100 1 056 1 156

Total 16 146 5 790 5 952

65 a

nd o

ver

Active 0 35 284 320

Inactive 73 1 488 1 561

Total 0 108 1 772 1 881

Opening Stock 10 623 1 625 508 714 1 221 4 791 1 133 5 924 326 1 527 1 853

Source: Table D.



- 27 -

6. Summary and Concluding remarks

The Social Accounting Matrix (SAM) and Socio-Demographic Matrix (SDM) are tools for working

with the activity of countries both empirically and theoretically, depending on whether they are

presented in a numerical or algebraic version. These are the so-called SAM-based and SDM-based

approaches for studying (measuring and modelling) the activity of countries.

Assuming that the core of the statistics representing the part of the activity of countries that can be

expressed in currency units (covered by the SAM), and in human beings (covered by the SDM), are

the national and the demographic accounts, respectively, at least as a starting point, their adoption is

recommended for any study that is looking for empirical evidence about that activity. This will enable

us to work with, and gain a greater knowledge about, the activity that is (supposedly) observed by the

national and the demographic accounts, which, both in a SAM and a SDM framework, will benefit

from the increased analytical content provided by the matrix format and the possibility of capturing

and working with networks of linkages not captured and worked on otherwise.

Numerical versions of those matrices can provide empirical descriptions of the reality under study,

whereas the corresponding algebraic versions can provide theoretical descriptions. From the former

matrix, the analysis of the activity of the country can be oriented in accordance with the purposes of

the study to be undertaken. From the latter, the performance of experiments will allow for the analysis

of scenarios that result from changes in those same realities. Although this paper focuses on the

numerical versions of both approaches, some references to work with algebraic versions are also

provided. Further research work is also envisaged into the possible combination of SAM and SDM-

based approaches.

Supported by the 2008 SNA, a basic SAM structure is proposed amounting to a summary set of the

flows that the SNA assumes to be observed and the controlling totals for other levels of

disaggregation. From that structure, it is possible to study specific aspects and maintain the

consistency of the whole system. The study of those specific aspects is made possible by the different

disaggregations and extensions that can be made or through the use of the aggregates, indicators and

balancing items that can be calculated.

In the accounts of that basic structure, represented by its rows and columns, besides the rest of the

world, the production and the (domestic) institutions are identified. The components of the production

accounts are: products (goods and services), activities (industries) and factors. The institutional

accounts, representing the institutional sectors, are broken down into current, capital and financial

accounts. In turn, the cells of that same basic structure are presented by blocks with common

characteristics, relating to the flows covered by the national accounts.



- 28 -

At other levels of disaggregation of these accounts, the blocks of cells will be converted into blocks

of submatrices. Working with those blocks is suggested as an easier way of constructing SAMs.

Disaggregations of the proposed SAM structure do not affect the consistency of the whole system.

Extensions, either from the national accounts or from other sources of information, pass through the

convenient adjustment to, or the connection with, the whole system in order to maintain its

consistency. This concern with consistency is a condition for ensuring that the network of linkages

that underlies the activity of countries is complete; in other words, besides the generation of income,

the distribution, redistribution and use of income, as well as the redistribution and accumulation of

wealth, have to be included. Such consistency is only possible when production and institutions are

worked on together. That network of linkages can only be identified and worked on in a matrix form

in a tool like the SAM, which can be worked on not only for the observed but also for the non-

observed activity of countries through the national accounts. The convenient coverage of that network

of linkages is a necessary condition for capturing multiplier effects in subsequent modelling, which

can provide important knowledge.

From the proposed SAM structure, it is also proposed that work should be performed outside the

matrix format with aggregates, indicators and balancing items, which can be seen as elements

extracted from our working tool in order to empirically highlight our purposes. Depending on the

detail of the SAM, we can therefore calculate more or less detailed aggregates, such as Gross

Domestic Product (GDP), Gross National Income, Disposable Income, etc. The same thing happens

in the case of the structural indicators of the functional and institutional distribution of generated

income, as well as the indicators of the use of disposable income. On the other hand, the ease with

which the main items in the revenue and expenditure of the institutional sectors and of the rest of the

world can be extracted from the respective rows and columns of the SAM can also be seen as a great

advantage.

Particularly when the focus of the study that is being undertaken is on the role played by the

households (within the institutional sectors) in the activity of a country during a pre-defined period

(usually a year), all that can be studied through the SAM can be further complemented with a SDM.

Representing the households, all the population in a country and the flows (expressed in currency

units) representing its production, its consumption and its income can be worked upon within a SAM

framework. In turn, when all the population in a country is worked upon within a SDM framework,

its movements (expressed in numbers of human beings) can be represented in the form of a stock-

flow matrix, which offers many possibilities for disaggregation. Establishing the connection between

the opening and the closing stock of the population for a particular period and the flows of people

during that period, births, deaths, immigration, emigration and changes between groups are the



- 29 -

movements that are recorded in a SDM. Depending on the purposes of the study, active or passive

sequences can be adopted to identify those groups. Usually identifying the different age groups is the

first step that should be taken prior to the definition of those sequences.

The matrices described in this paper can be either the numerical versions of the reality under study or

their replication(s) after running a SAM or SDM-based model(s) in order to try out policy measures

or other types of changes and to identify the corresponding macroeconomic effects. In the case of

replication(s), we will have one or more scenarios representing the impacts of those policy measures,

which, when compared with the reality under study, can support the processes of policy decision-

making and policy decision-taking.

With or without the proposed structures, when the activity of countries has to be studied, the empirical

work of measurement and modelling, the matrix format and the use of the national and demographic

accounts are all recommended. Those accounts can be considered as a starting point for the use of

other sources of information and for the inclusion of other dimensions. In order to do this, in the case

of the national accounts, it would be convenient if the compilers of countries were to give the same

importance to the institutional accounts as they give to the production accounts. It would also be

convenient if they made the results of their work and the methodological details underlying their work

available, namely the “from whom to whom” matrices and the manuals about sources and

methodologies, in order to enable their free use and evaluation by potential users (international

organisations, students, researchers, etc.). The last recommendation could also be extended to the

demographic accounts. This would certainly be a contribution towards developing our knowledge of

the activity of countries, especially where there are problems of poverty and inequalities in the

distribution of income, with the consequent need for special attention to be paid to the households.

This proposal is intended to contribute towards a more detailed and complete study of the activity of

countries, with greater knowledge being provided about the whole and the corresponding interactions

of its parts. This will allow for subsequent interventions to be carried out in relation to the parts while

remaining aware of the impacts that this will have on the whole.

This is what the author of this paper considers to be a possible way of introducing empirical evidence

into the work being carried out at the macroeconomic level, where the network of linkages within the

socioeconomic groups that intervene in the activity of countries should not continue to be neglected

so completely. The adoption of this principle could even ensure the greater commitment on the part

of countries to adopt and adapt systems of national and demographic accounts, with greater

collaboration between macroeconomists and statisticians.



- 30 -

References

Inter-Secretariat Working Group on National Accounts (United Nations, European Commission,

International Monetary Fund, Organisation for Economic Cooperation and Development and World

Bank) – ISWGNA, System of National Accounts 2008, Series F, No. 2, Rev. 5, United Nations, New

York, 2009.

Keuning S. and Ruijter W., “Guidelines to the construction of a Social Accounting Matrix”, Review

of Income and Wealth, 34, 71-100, 1988.

Lequiller F., Blades D., Understanding National Accounts, Organisation for Economic Co-operation

and Development (OECD), Paris, France, 2006.

Pyatt, G., “Some Early Multiplier Models of the Relationship between Income Distribution and

Production Structure”, Economic Systems Research, 13, 139-163, 2001.

Pyatt, G., “Some Relationships between T-Accounts, Input-Output Tables and Social Accounting

Matrices”, Economic Systems Research, 11, 365-387, 1999.

Pyatt, G., “Fundamentals of Social Accounting”, Economic Systems Research, 3, 315-341, 1991.

Pyatt, G., “SAMs, the SNA and National Accounting Capabilities”, Review of Income and Wealth,

37, 177-198, 1991a.

Pyatt, G., “A SAM Approach to Modeling”, Journal of Policy Modeling, 10, 327-352, 1988.

Pyatt, G., “Commodity Balances and National Accounts: a SAM Perspective”, Review of Income and

Wealth, 31, 155-169, 1985.

Pyatt, G. and Roe, A., Social Accounting for Development Planning with Special Reference to Sri

Lanka, Cambridge University Press, Cambridge, UK, 1977.

Pyatt, G. and Round, J., “Distributional Invariance and the Design of SAMs”, Economic Systems

Research, 24, 251-273, 2012

Pyatt, G. and Round, J., “Accounting and Fixed Price Multipliers in a Social Accounting Matrix

Framework”, in G. Pyatt, and J. Round, (coord.), Social Accounting Matrices. A Basis for Planning.

A World Bank Symposium, World Bank, 52-69, 1985.

Round, J., “Constructing SAMs for Development Policy Analysis: Lessons Learned and Challenges

Ahead”, Economic Systems Research, 15, 161-183, 2003.



- 31 -

Round, J., “The Structure of the European Economy: a SAM Perspective”, in J. Round, (ed.), The

European Economy in Perspective. Essays in Honour of Edward Nevin, University of Wales Press,

Cardiff, 59-83, 1994.

Round, J., “A SAM for Europe: Problems and Perspectives”, Economic Systems Research, 3, 249-

268, 1991.

Santos S., “A quantitative approach to the effects of social policy measures. An application to

Portugal, using Social Accounting Matrices”, EERI (Economics and Econometrics Research

Institute) RP (Research Papers) 2010/33; MPRA (Munich Personal RePEc Archive) Paper No. 23676,

2010.

Santos S., From the System of National Accounts (SNA) to a Social Accounting Matrix (SAM)-Based

Model. An Application to Portugal, Edições Almedina, Coimbra-Portugal, 2009.

Santos S., “Modelling Economic Circuit Flows in a Social Accounting Matrix Framework. An

Application to Portugal”, Applied Economics, 39, 1753-1771, 2007.

Santos S., “Portuguese net borrowing and the government budget balance. A SAM approach”,

Journal of Policy Modeling, 26, 703-717, 2004.

Stone, R., “Nobel Memorial Lecture 1984. The Accounts of Society”, Journal of Applied

Econometrics, 1(1), 5-28, 1986.

Stone, R., “Demographic Input-Output: An Extension of Social Accounting”, in: I.Sohn (coord),

Readings in Input-Output Analysis: Theory and Applications, Oxford University Press, USA, 151-

172, 1986a.

Stone, R., “The Disaggregation of the household Sector in the National Accounts”, in G. Pyatt, and

J. Round, (coord.), Social Accounting Matrices. A Basis for Planning. A World Bank Symposium,

World Bank, 145 - 185, 1985.

Stone, R., “Working with what we have: how can existing data be used in the construction and

analysis of socio-demographic matrices?”, Review of Income and Wealth, 28(3), 291-303, 1982.

Stone, R., Aspects of Economic and Social Modelling, Editions Droz, Genéve (Suisse), 154p, 1981.

Stone, R., “Towards a System of Social and Demographic Statistics”, Studies in Methods, Series F,

Nº18, United Nations, New York, 198p, 1975.

Stone, R., “A System of Social Matrices”, Review of Income and Wealth, 19(3), 143-166, 1973.



- 32 -

Stone, R., “An Integrated System of Demographic, Manpower and Social Statistics and its Links with

the System of National Economic Accounts”, Sankhyā: The Indian Journal of Statistics, 33(1-2), 1-

184, 1971.

Stone, R., “The Social Accounts from a consumer's point of view. An outline and discussion of the

revised United Nations System of National Accounts”, Review of Income and Wealth, 12(1), 1-33,

1966.



- 33 -

Appendixes



- 34 -

S.2 S.1 S.15 S.14 S.13 S.12 S.11

Total

Goods and

Services

Account

(Resources)

Rest of

the World

Account

Total of

the

Economy

NPISHs HouseholdsGeneral

Government

Financial

Corporations

Non-

Financial

Corporations Code

Transactions and other flows,

stocks and balancing items

59 717 59 717 P.7 Imports of goods and services

47 236 47 236 P.6 Exports of goods and services

311 365 311 365 P.1 Output of goods and services

162 661 162 661 2 394 12 470 8 390 5 238 134 170 P.2 Intermediate consumption

19 800 19 800 19 800 D.21-D.31 Net taxes on products

168 504 168 504 2 896 29 827 24 491 10 487 81 001 B.1g/B.1*g Gross added value/gross

domestic product

29 795 29 795 565 9 145 3 585 739 15 761 K.1 Consumption of fixed capital

138 708 138 708 2 331 20 682 20 907 9 748 65 240 B.1n/B.1*n Value added, net/Net domestic

product

12 482 12 482 B.11 External balance of goods and

services

86 127 239 85 888 2 633 5 284 21 386 4 260 52 325 D.1 Compensation of employees

19 100 19 100 - 300 65 - 390 28 - 103 D.2-D.3 Net taxes on production and

imports

19 800 19 800 D.21-D.31 Net taxes on products

- 700 - 700 - 300 65 - 390 28 - 103 D.29-D.39 Net taxes on production

45 770 45 770 563 6 734 3 495 6 199 28 779 B.2g Gross operating surplus

17 745 17 745 17 745 B.3g Gross mixed income

18 452 18 452 - 2 66 - 89 5 460 13 018 B.2n Net operating surplus

15 268 15 268 15 268 B.3n Net mixed income

57 187 8 800 48 387 45 3 847 4 820 17 996 21 679 D.4 Property income

161 639 161 639 837 120 015 20 182 5 990 14 615 B.5g Gross national income/ Gross

balance of primary incomes

131 844 131 844 272 110 870 16 598 5 251 - 1 147 B.5n Net national income/ Net balance

of primary incomes

15 176 32 15 145 5 10 137 8 637 4 358 D.5 Current taxes on income, wealth,

etc

26 791 109 26 682 26 682 D.61 Social contributions

34 257 46 34 210 52 42 28 659 3 627 1 830 D.62 Social benefits other than social

transfers in kind

17 299 4 394 12 904 92 3 952 4 274 2 347 2 240 D.7 Other current transfers

162 800 162 800 3 214 119 745 25 466 5 472 8 903 B.6g Gross disposable income

133 004 133 004 2 648 110 600 21 881 4 733 - 6 858 B.6n Net disposable income

23 963 23 963 3 568 20 396 D.63 Social transfers in kind

162 800 162 800 - 354 143 708 5 070 5 472 8 903 B.7g Gross adjusted disposable

income

133 004 133 004 - 919 134 564 1 485 4 733 - 6 858 B.7n Net adjusted disposable income

162 800 162 800 3 214 119 745 25 466 5 472 8 903 B.6g Gross disposable income

133 004 133 004 2 648 110 600 21 881 4 733 - 6 858 B.6n Net disposable income

146 934 146 934 130 170 16 765 P.4 Actual Final Consumption

146 934 146 934 3 568 106 206 37 160 P.3 Final consumption expenditure

189 189 189 D.8 Adjustment for the change in the

net equity of households in

pension funds reserves

15 865 15 865 - 354 13 728 - 11 695 5 283 8 903 B.8g Gross saving

- 13 930 - 13 930 - 919 4 583 - 15 279 4 543 - 6 858 B.8n Net saving

18 186 18 186 B.12 Current external balance

B.8g Gross saving

B.8n Net saving

B.12 Current external balance

D.9 Capital transfers, receivable

D.9 Capital transfers, payable (-)

4 256 16 217 - 11 962 - 564 4 833 - 15 476 4 485 - 5 241 B.10.1 Changes in net worth due to

saving and capital transfers

34 051 34 051 834 7 269 5 071 1 064 19 812 P.5 Gross capital formation

- 29 795 - 29 795 - 565 - 9 145 - 3 585 - 739 - 15 761 K.1 Consumption of fixed capital (-)

- 4 4 8 - 2 295 173 3 2 116 K.2 Acquisitions less disposals of

non-produced non-financial

assets

16 222 - 16 222 - 840 9 004 - 17 135 4 157 - 11 407 B.9 Net lending (+) /borrowing (-)

S.2 S.1 S.13 S.12 S.11

93 794 37 209 56 586 1 059 37 866 5 376Net acquisition of financial

assets\

Net incurrence of liabilities

11 - 11 - 11 F.1 Monetary gold and SDRs

6 430 4 242 2 188 - 506 1 783 - 173 F.2 Currency and deposits

49 697 28 529 21 168 325 20 617 109 F.3 Securities other than shares

8 781 - 763 9 544 - 192 8 071 1 850 F.4 Loans

18 312 4 529 13 783 1 001 3 696 1 205 F.5 Shares and other equity

4 762 5 4 757 57 62 F.6 Insurance technical reserves

5 812 655 5 158 431 3 654 2 322 F.7

Other accounts

receivable/payable

B.9 F Net lending (+) /borrowing (-)

Current accounts

Uses

Accounts

I. Production /

external account

of goods and

services

II.1

.Pri

ma

ry d

istr

ibu

tio

n o

f in

com

e

acc

ou

nts

II.1.1.

Generation

of income

account

II.1.2.

Allocation

of primary

income

account

II.2. Secondary

distribution

income account

II.3.

Redistribution of

income in kind

account

II.4. Use of income

account

Accumulation accounts

Changes in Assets

III.

1. C

ap

ita

l acc

ou

nts

III.1.1.

Change in

net worth

due to

saving and

capital

transfers

III.1.2

Acquisition

s of non-

financial

assets

account

S.15 + S.14

III.2 Financial

account

12 284

1 084

116

- 186

7 880

4 638

- 1 249

Table A. Integrated Economic Accounts Table for Portugal in 20095 (unit: 106 euros)

5 This table still uses the 1993 SNA terminology. Its form is the one usually made available by Statistics Portugal, to

which the author added the financial account, made available separately by the Portuguese Central Bank.



- 35 -

S.11 S.12 S.13 S.14 S.15 S.1 S.2

Code

Transactions and other flows,

stocks and balancing itemsNon-

Financial

Corporations

Financial

Corporations

General

GovernmentHouseholds NPISHs

Total of

the

Economy

Rest of

the

World

Account

Goods and

Services

Account

(Uses)

Total

P.7 Imports of goods and services 59 717 59 717

P.6 Exports of goods and services 47 236 47 236

P.1 Output of goods and services 215 171 15 725 32 881 42 297 5 290 311 365 311 365

P.2 Intermediate consumption 162 661 162 661

D.21-D.31 Net taxes on products 19 800 19 800

B.1g/B.1*g Gross added value/gross

domestic product

81 001 10 487 24 491 29 827 2 896 168 504 168 504

K.1 Consumption of fixed capital

B.1n/B.1*n Value added, net/Net domestic

product

65 240 9 748 20 907 20 682 2 331 138 708 138 708

B.11 External balance of goods and

services

12 482 12 482

D.1 Compensation of employees 85 757 85 757 370 86 127

D.2-D.3 Net taxes on production and

imports

20 216 20 216 - 1 116 19 100

D.21-D.31 Net taxes on products 19 694 19 694 106 19 800

D.29-D.39 Net taxes on production 522 522 - 1 222 - 700

B.2g Gross operating surplus 28 779 6 199 3 495 6 734 563 45 770 45 770

B.3g Gross mixed income 17 745 17 745 17 745

B.2n Net operating surplus 13 018 5 460 - 89 66 - 2 18 452 18 452

B.3n Net mixed income 15 268 15 268 15 268

D.4 Property income 7 514 17 787 1 291 13 626 319 40 538 16 649 57 187

B.5g Gross national income/ Gross

balance of primary incomes

14 615 5 990 20 182 120 015 837 161 639 161 639

B.5n Net national income/ Net balance

of primary incomes

- 1 147 5 251 16 598 110 870 272 131 844 131 844

D.5 Current taxes on income, wealth,

etc

15 146 15 146 30 15 176

D.61 Social contributions 1 830 3 773 21 031 42 52 26 728 64 26 791

D.62 Social benefits other than social

transfers in kind

34 081 34 081 176 34 257

D.7 Other current transfers 887 2 320 2 047 6 421 2 474 14 148 3 151 17 299

B.6g Gross disposable income 8 903 5 472 25 466 119 745 3 214 162 800 162 800

B.6n Net disposable income - 6 858 4 733 21 881 110 600 2 648 133 004 133 004

D.63 Social transfers in kind 23 963 23 963 23 963

B.7g Gross adjusted disposable

income

8 903 5 472 5 070 143 708 - 354 162 800 162 800

B.7n Net adjusted disposable income - 6 858 4 733 1 485 134 564 - 919 133 004 133 004

B.6g Gross disposable income 8 903 5 472 25 466 119 745 3 214 162 800 162 800

B.6n Net disposable income - 6 858 4 733 21 881 110 600 2 648 133 004 133 004

P.4 Actual Final Consumption 146 934 146 934

P.3 Final consumption expenditure 146 934 146 934

D.8 Adjustment for the change in the

net equity of households in

pension funds reserves

189 189 189

B.8g Gross saving

B.8n Net saving

B.12 Current external balance

B.8g Gross saving 8 903 5 283 - 11 695 13 728 - 354 15 865 15 865

B.8n Net saving - 6 858 4 543 - 15 279 4 583 - 919 - 13 930 - 13 930

B.12 Current external balance 18 186 18 186

D.9 Capital transfers, receivable 1 719 77 1 246 369 358 3 769 264 4 033

D.9 Capital transfers, payable (-) - 102 - 135 - 1 442 - 119 - 2 - 1 801 - 2 232 - 4 033

B.10.1 Changes in net worth due to

saving and capital transfers

- 5 241 4 485 - 15 476 4 833 - 564 - 11 962 16 217 4 256

P.5 Gross capital formation 34 051 34 051

K.1 Consumption of fixed capital (-)

K.2 Acquisitions less disposals of

non-produced non-financial

assets

B.9 Net lending (+) /borrowing (-)

S.11 S.12 S.13 S.1 S.2

Net acquisition of financial

assets\

Net incurrence of liabilities 17 420 34 082 18 199 73 868 19 926 112 824

F.1 Monetary gold and SDRs

F.2 Currency and deposits 6 063 - 532 5 532 898 29 818

F.3 Securities other than shares 2 102 16 412 16 235 34 749 14 948 28 663

F.4 Loans 4 565 - 2 867 1 640 6 352 2 429 34 711

F.5 Shares and other equity 6 745 10 521 17 266 1 046 5 407

F.6 Insurance technical reserves - 140 4 845 4 705 57 5 929

F.7 Other accounts

receivable/payable 4 148 - 892 855 5 263 549

8 296

B.9 F Net lending (+) /borrowing (-) - 12 044 3 784 - 17 139 - 17 282 17 282

Statistical discrepancy - 636 - 374 - 4 - 1 061 1 061

Current accounts

Resources

Accounts

I. Production /

external account

of goods and

services

II.1.1.

Generation

of income

account

II.1.P

rima

ry d

istribu

tion

of in

com

e acco

un

ts

II.1.2.

Allocation

of primary

income

account

II.2. Secondary

distribution

income account

II.3.

Redistribution of

income in kind

II.4. Use of

income account

Accumulation accounts

Changes in liabilities and net worth

III.1.1.

Change in

net worth

due to

saving and

III.1.C

ap

ital A

ccou

nts

III.1.2

Acquisitio

ns of non-

financial

assets

account

S.14 + S.15

4 167

3 015

1 152

8 117

- 47

Sources: Statistics Portugal (INE ); Portuguese Central Bank (Banco de Portugal )

III.2 Financial

account

Table A (continued). Integrated Economic Accounts Table for Portugal in 2009 (Unit: 106 euros)


- 36 -

Table B. Connection between the totals of the current transactions block of the SAM and the Integrated Economic Accounts Table for Portugal in

2009

(Unit: 106 euros)

Source: Table 3 and Appendix A.



- 37 -

Table C: Statistical sources used for the construction of the numerical version of the SDMs for

Portugal in 2009


Age

group

Total Population

Deaths Births

(surviving) Immigrants Emigrants

Active Inactive Total

2008

0-14 − 1,624.600 1,624.600 0.575 104.594 5.541 5.314

15-24 507.500 713.800 1,221.300 0.514 − 9.508 5.480

25-64 4,791.300 1,132.500 5,923.800 17.599 − 14.254 9.210

65 and over 326.000 1,527.000 1,853.000 85.572 − 0.415 0.353

Total 5,624.800 4,997.900 10,622.700 104.260 104.594 29.718 20.357

2009

0-14 − 1,615.000 1,615.000 0.579 99.491 5.941 4.409

15-24 466.300 723.900 1,190.200 0.501 − 10.332 4.547

25-64 4,796.700 1,155.700 5,952.400 17.694 − 15.600 7.648

65 and over 319.700 1,561.100 1,880.800 80.425 − 0.434 0.295

Total 5,582.700 5,055.700 10,638.400 99.199 99.491 32.307 16.899

Source: Statistics Portugal (INE) – Demographic Statistics, Labour Force Survey.

D. Methodology adopted in the construction of the numerical version of the SDMs for Portugal

in 2009

The SDMs at the two levels of disaggregation were constructed from the inflows and outflows

identified in Table D – constructed from Table C. From Table D, the inflows are represented in the

rows and the outflows in the columns of the SDMs (Tables 8 and 9), whose diagonals (represented in

italic font) are calculated in the matrices themselves through the difference between the closing stock

and the other flows in a row or between the opening stock and the other flows in a column.

When information is missing or whenever inconsistencies are found, the following assumptions are

adopted:

- the α (scalar), as described in Table 7, is zero;

- all emigrants and immigrants aged 15 and over are active;

- those moving from one age group to another and those surviving in the same age group maintain

the same situation regarding their economic activity;

- deaths by economic activity are proportional to the opening activity (inactivity) rates.



- 38 -

Table D. Portugal in 2009 – inflows and outflows of the population by age group (first level of

disaggregation) and economic activity (second level of disaggregation)


Age group 0-14: Total

Inflows Outflows

Survivors from last

year (Opening Stock)

1,624.600 Deaths 0.579

Births 99.491 Emigrants 4.409

Immigrants 5.941 Movers to the age of

15

110.044

Survivors into next

year (Closing

Stock)

1,615.000

Total 1,730.032 Total 1,730.032


Inflows Outflows

Survivors from last


1,221.300 Deaths 0.501

Immigrants 10.332 Emigrants 4.547

Entrants from the age

of 14

110.044 Movers to the age of

25

146.428

Survivors into next

year (Closing

Stock)

1,190.200

Total 1,341.676 Total 1,341.676

Age group 15-24: Active

Inflows Outflows

Survivors from last


507.500 Deaths 0.208


Movers to the age of

25

46.777

Survivors into next

year (Closing

Stock) 466.300

Total 517.832 Total 517.832



- 39 -

Age group 15-24: Inactive

Inflows Outflows

Survivors from last


713.800 Deaths 0.293


of 14


25

99.651

Survivors into next

year (Closing

Stock)

723.900

Total 823.844 Total 823.844


Inflows Outflows

Survivors from last


5,923.800 Deaths 17.694



of 24


65

108.086

Survivors into next

year (Closing

Stock)

5,952.400

Total 6,085.828 Total 6,085.828

Age group 25-64: Active

Inflows Outflows

Survivors from last


4,791.300 Deaths 14.311



of 24


65

35.018

Survivors into next

year (Closing

Stock)

4,796.700

Total 4,853.677 Total 4,853.677



- 40 -

Age group 25-64: Inactive

Inflows Outflows

Survivors from last


1,132.500 Deaths 3.383


of 24


65

73.068

Survivors into next

year (Closing

Stock)

1,155.700

Total 1,232.151 Total 1,232.151

Age group 65 and over: Total

Inflows Outflows

Survivors from last


1,853.000 Deaths 80.425



of 64

108.086 Survivors into next

year (Closing Stock)

1,880.800

Total 1,961.520 Total 1,961.520

Age group 65 and over: Active

Inflows Outflows

Survivors from last


326.000 Deaths 41.457



of 64


year (Closing Stock)

319.700

Total 361.452 Total 361.452

Age group 65 and over: Inactive

Inflows Outflows

Survivors from last


1,527.000 Deaths 38.968


of 64


year (Closing Stock) 1,561.100

1,600.068 Total 1,600.068



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Outside World

Inflows Outflows

Deaths 99.199 Births 99.491

Emigrants 16.899 Immigrants 32.307

Survivors into next

year (Our Country's

Closing Stock)

10,638.400 Survivors from the

last year (Our

Country's Opening

Stock)

10,622.700

Total 10,754.498 Total 10,754.498

Source: Table C.

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